Previously the asymptotics (REF ) were known for \(h,k \in \lbrace 0,1,2\rbrace \)  with \(h\le k\)  due to Ingham [1]} and Conrey [2]}, and upper bounds of the right order were only known for half integer valued \(h,k \le 2\)  due to work of Conrey [2]} and Conrey Ghosh [4]}.
The aim of this paper is to establish upper bounds for \(I_T (k,h)\)  and \(J_T(k,h)\)  of the right order in a larger range of \(h\)  and \(k\) .
